All things being Equal

[frost]

hello


i have another question..


we all know that an EC is twice as likely to hit one time as it is to hit twice in a row and for it to hit two times in a row it is twice as likely to this than land three times in a row etc..


my question is


would we get the same results from 100 spins that we would get from 1000 spins or maybe more?


would we get a bigger difference (maybe 2 in a row is 3 times more likely to hit than 3 in a row) from a smaller sample or a bigger sample?


how far can results deviate from 'twice as likely'?


if i used the same amount of spins an investigated them would you more than likely get the same result all the time?


is there anywhere i can find out the answers to these questions or somewhere where i could do further studies?


thank you in advance fro your replies 

[Bayes]

Hi frost,

Generally speaking, in smaller samples, you're going to get more 'out of balance' results, so in 100 spins the difference is likely to be larger than in 1000 spins (the law of large numbers).

How far can results deviate?  I don't know, but it's a good question. I've seen sequences where you don't get a series of 2 (only singles and series > 2) for 50+ spins. There's a statistical test for randomness called the 'Runs test' which takes into account the standard deviations of 'runs', so that might be a good place to start doing some research.

I've actually been meaning to post it here but haven't got around to it yet. If I get time in the next couple of days I'll post the details.

[frost]

thank you bayes.

[frost]

Hello eveyone


What if we had determind values?


So we take line 5 for example


This line can show a minimum of 1 time and a maximum of 6 times in a row. if we were to look at what happens in say 2000 spins is there a formula could use to work out this problem?


Also what topic does this come under? looked at the runs test but in order to use that would need to have the results ready


Am correct in my thinking?

[GARNabby]

Generally speaking, in smaller samples, you're going to get more 'out of balance' results, so in 100 spins the difference is likely to be larger than in 1000 spins (the law of large numbers).

And with the lesser-chance bets.  The higher the win/lose-odds, the lower/higher the SD.  That's why it's so much easier to fall into the "trap" of perceiving peculiar distributions from the inside play of roulette.

[frost]

what is the name of the topic i should look at in order to answer my question?

i no its statistics but what?

[GARNabby]

frost,

i will try to post up some of the specific math here about these SD's in a day or two, if i can locate it from my drives.  (It's quite-difficult to find the sort of stuff that you can "get your hands on" off the internet.  Lots of complex theory, but little direct application.)

I returned to this site, tonight, to only clean up the wording in my previous post.

[frost]

okay.

thank you garnabby

[Bayes]

So we take line 5 for example


This line can show a minimum of 1 time and a maximum of 6 times in a row. if we were to look at what happens in say 2000 spins is there a formula could use to work out this problem?

frost,

What exactly is the question you want an answer to? do you want to know the number of series of 1-in-a-row, 2-in-a-row etc for lines? In other words, you want some relationship between series for lines as there is for an even chance bet, right?

[Bayes]

For an EC bet, each series is half as likely as the previous one, ie; a series of 3 is half as likely as a series of 2. For a line, each series (streak) is one sixth as likely (ignoring the zero) as the previous.

ie; for an EC, the probabilities are: 1/2, (1/2)², (1/2)³, (1/2)⁴...

for a line, they are: 1/6, (1/6)², (1/6)³, (1/6)⁴...

[frost]

frost,

What exactly is the question you want an answer to? do you want to know the number of series of 1-in-a-row, 2-in-a-row etc for lines? In other words, you want some relationship between series for lines as there is for an even chance bet, right?

not entierly but please continue with your idea, it might spark something off.


my idea was this. we will use RED for the example.


in a series of spins we will have results like this


red land once - 100
red land twice - 52
red land three times - 25
red land four times - 12


etc


what i expected is these results to roughly remain the same reguardless of our sample size. if we used 1000 or 10000 spins we will still see that for a red to land 2 times in a row it will still be half as likely as a single red to show.


now i wanted to know

   
• how far away from the expected value (half as much) can the results go?
• am i right in thinking that no matter the amount of spins used we will always get the same trend of results?
• if there a formula i can use to work out the above questions?
• what kind of statistics should i be looking at to get a better understanding of what i want to know?
• what is the meaning of life?

thank you

[Skakus]

   
• what is the meaning of life?

thank you

42

[Bayes]

Ha!, you beat me to it Skakus, I was about to post the same reply.     (if you don't know what this means, look up 'The Hitch-Hiker's Guide to the Galaxy').

@ frost,

Ok, so as I said in a previous post, you definitely will NOT get a nice even distribution with small sample sizes. In 100 spins you may only get 30 singles instead of the 'required' 50.

You can calculate the standard deviation (z-score) using the standard formula if you're only interested in how ONE series compares with the remaining (higher series). This is because you're only concerned with 2 outcomes. ie; since there are as many series of 1 (singles) as series higher than 1 (including series of 2,3,4...) then the probability is 0.5 for there to be as many series of 1 as remaining series in any sample. This applies no matter how far up the series you start. e.g. suppose you ignore singles and want to compare the number of series of 2 with the number of series higher than 2 - the probability that there will be equal numbers is still 0.5. And so on for any particular series you're interested in.

So in my example above of 30 singles in 100 spins, this is the same (from a probability point of view) as getting 30 reds in sample of 100, which has a z-score of around -4.0 - pretty rare.

However, if you want to take all series together (not just comparing one series with all higher series), then it gets more complicated. The maths isn't simple, but look up 'Multinomial Distribution'. There's a calculator here.

[monaco]

in 100 spins, you would expect to get around 25 singles wouldn't you?
25 singles = 25 spins
12 doubles = 24 spins
6 trebles = 18 spins
3 4's = 12 spins
2 5's = 10 spins
1 6 = 6 spins

there or thereabouts?

[Bayes]

monaco, you're right. In my previous post I shouldn't have said 'spins' but total streaks, so the total singles is 50%, which of course isn't the same as accounting for 50 spins out of 100. 

Nevertheless, the principle holds good.